%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP413-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:39:45 PM UTC 2026
% Result : Unsatisfiable 14.71s 3.26s
% Output : CNFRefutation 14.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 2
% Syntax : Number of clauses : 44 ( 44 unt; 0 nHn; 5 RR)
% Number of literals : 44 ( 43 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 125 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(multiply(X1,inverse(X2))),X3))),X2))) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(c_0_2,axiom,
multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(multiply(X1,inverse(X2))),X3))),X2))) = X3,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(X3)),X2))) = inverse(multiply(multiply(multiply(inverse(X4),X4),inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(X2))),inverse(X4))),X3))),X4)),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(X3))),inverse(X1))),multiply(inverse(multiply(X2,inverse(X3))),X4)))),X1)) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(X3)),X2)))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_6,plain,
inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X2,inverse(X1))),multiply(X2,X3)))),X1)) = X3,
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_7,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X3)) = multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,X3)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(X4,X2)),multiply(X4,X3)),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_9,plain,
multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),multiply(X3,inverse(multiply(multiply(multiply(inverse(X4),X4),inverse(X5)),X4)))),X2))) = inverse(multiply(multiply(multiply(inverse(X6),X6),inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(X2))),inverse(X6))),multiply(multiply(multiply(inverse(X7),X7),inverse(multiply(inverse(multiply(inverse(multiply(X3,inverse(X4))),inverse(X7))),X5))),X7)))),X6)),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_10,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(X4,multiply(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(multiply(X5,inverse(X2))),multiply(X5,X4)))),X3)),
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_11,plain,
inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,X3)))),X1)) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_2]),c_0_2]) ).
cnf(c_0_12,plain,
multiply(multiply(multiply(inverse(inverse(X1)),inverse(X1)),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(X3))),inverse(inverse(X1)))),X4))),inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(multiply(X2,inverse(multiply(multiply(multiply(inverse(X3),X3),inverse(X4)),X3))),X5))),X1))) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_13,plain,
inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(X2),X2))),X1)) = inverse(X1),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(X2),X2))),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_13]),c_0_5]) ).
cnf(c_0_15,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X2)) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_16,plain,
multiply(inverse(inverse(X1)),inverse(X1)) = multiply(inverse(X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_14]),c_0_15]) ).
cnf(c_0_17,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_16,c_0_16]) ).
cnf(c_0_18,plain,
multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(X2),X2))),X3) = X3,
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_19,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_18]),c_0_18]) ).
cnf(c_0_20,plain,
multiply(X1,multiply(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(inverse(X2)),X1))),X3)) = multiply(inverse(X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_19]),c_0_19]) ).
cnf(c_0_21,plain,
multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X2),X3)) = multiply(inverse(X2),X3),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_22,plain,
multiply(inverse(inverse(X1)),inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(X2)),X1))) = X2,
inference(rw,[status(thm)],[c_0_5,c_0_19]) ).
cnf(c_0_23,plain,
inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(inverse(X1)),X2))),X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_18]),c_0_18]) ).
cnf(c_0_24,plain,
multiply(X1,multiply(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X3),X1))),X4)) = multiply(X3,X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_6]),c_0_19]),c_0_20]) ).
cnf(c_0_25,plain,
multiply(inverse(multiply(inverse(X1),X1)),X2) = X2,
inference(spm,[status(thm)],[c_0_21,c_0_2]) ).
cnf(c_0_26,plain,
multiply(inverse(inverse(X1)),inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(X3)),X1))) = X3,
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_27,plain,
multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),X3),X2))) = inverse(multiply(multiply(multiply(inverse(X4),X4),inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(X2))),inverse(X4))),multiply(multiply(multiply(inverse(X5),X5),inverse(multiply(inverse(inverse(X5)),X3))),X5)))),X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_6]),c_0_19]) ).
cnf(c_0_28,plain,
inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(inverse(X2)),X3))),X2)) = X3,
inference(spm,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_29,plain,
multiply(X1,multiply(multiply(multiply(inverse(X2),X2),inverse(X1)),X3)) = multiply(multiply(inverse(X4),X4),X3),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(inverse(X1)),inverse(X2)))),X1) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_25]),c_0_28]) ).
cnf(c_0_31,plain,
multiply(multiply(inverse(inverse(X1)),inverse(X2)),X2) = multiply(multiply(inverse(X3),X3),X1),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,plain,
multiply(multiply(inverse(inverse(X1)),inverse(X2)),X2) = multiply(multiply(inverse(inverse(X1)),inverse(X3)),X3),
inference(spm,[status(thm)],[c_0_31,c_0_31]) ).
cnf(c_0_33,plain,
inverse(multiply(multiply(multiply(inverse(multiply(X1,X2)),multiply(X1,X2)),inverse(multiply(inverse(multiply(X3,inverse(multiply(X4,X2)))),multiply(X3,X5)))),multiply(X4,X2))) = X5,
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_34,plain,
multiply(multiply(inverse(X1),inverse(X2)),X2) = multiply(multiply(inverse(X1),inverse(X3)),X3),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,plain,
multiply(multiply(X1,inverse(X2)),X2) = multiply(multiply(X1,inverse(X3)),X3),
inference(spm,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(fof_simplification,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_0_37,plain,
multiply(multiply(multiply(inverse(X1),X1),inverse(X2)),X2) = multiply(inverse(X3),X3),
inference(spm,[status(thm)],[c_0_18,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
c_0_36 ).
cnf(c_0_39,plain,
multiply(multiply(multiply(inverse(inverse(inverse(multiply(inverse(X1),X1)))),inverse(X2)),X2),X3) = X3,
inference(spm,[status(thm)],[c_0_18,c_0_31]) ).
cnf(c_0_40,plain,
multiply(inverse(inverse(X1)),inverse(multiply(inverse(X2),X2))) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
multiply(multiply(inverse(X1),X1),a2) != a2,
inference(spm,[status(thm)],[c_0_38,c_0_17]) ).
cnf(c_0_42,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_25]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP413-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:15:01 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.71/3.26 % Version: 3.5.1
% 14.71/3.26 % Preprocessing class: FSSSSMSSSSSNFFN.
% 14.71/3.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.71/3.26 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 14.71/3.26 % Starting new_bool_3 with 300s (1) cores
% 14.71/3.26 % Starting new_bool_1 with 300s (1) cores
% 14.71/3.26 % Starting sh5l with 300s (1) cores
% 14.71/3.26 % new_bool_3 with pid 1610920 completed with status 0
% 14.71/3.26 % Result found by new_bool_3
% 14.71/3.26 % Preprocessing class: FSSSSMSSSSSNFFN.
% 14.71/3.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.71/3.26 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 14.71/3.26 % Starting new_bool_3 with 300s (1) cores
% 14.71/3.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 14.71/3.26 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 14.71/3.26 % Search class: FUUPF-FFSF21-DFFFFFNN
% 14.71/3.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 14.71/3.26 % Starting SubtermCWHack with 31s (1) cores
% 14.71/3.26 % SubtermCWHack with pid 1610923 completed with status 0
% 14.71/3.26 % Result found by SubtermCWHack
% 14.71/3.26 % Preprocessing class: FSSSSMSSSSSNFFN.
% 14.71/3.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.71/3.26 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 14.71/3.26 % Starting new_bool_3 with 300s (1) cores
% 14.71/3.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 14.71/3.26 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 14.71/3.26 % Search class: FUUPF-FFSF21-DFFFFFNN
% 14.71/3.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 14.71/3.26 % Starting SubtermCWHack with 31s (1) cores
% 14.71/3.26 % Preprocessing time : 0.002 s
% 14.71/3.26
% 14.71/3.26 % Proof found!
% 14.71/3.26 % SZS status Unsatisfiable
% 14.71/3.26 % SZS output start CNFRefutation
% See solution above
% 14.71/3.26 % Parsed axioms : 2
% 14.71/3.26 % Removed by relevancy pruning/SinE : 0
% 14.71/3.26 % Initial clauses : 2
% 14.71/3.26 % Removed in clause preprocessing : 0
% 14.71/3.26 % Initial clauses in saturation : 2
% 14.71/3.26 % Processed clauses : 503
% 14.71/3.26 % ...of these trivial : 47
% 14.71/3.26 % ...subsumed : 350
% 14.71/3.26 % ...remaining for further processing : 106
% 14.71/3.26 % Other redundant clauses eliminated : 0
% 14.71/3.26 % Clauses deleted for lack of memory : 0
% 14.71/3.26 % Backward-subsumed : 6
% 14.71/3.26 % Backward-rewritten : 30
% 14.71/3.26 % Generated clauses : 42983
% 14.71/3.26 % ...of the previous two non-redundant : 41583
% 14.71/3.26 % ...aggressively subsumed : 0
% 14.71/3.26 % Contextual simplify-reflections : 0
% 14.71/3.26 % Paramodulations : 42983
% 14.71/3.26 % Factorizations : 0
% 14.71/3.26 % NegExts : 0
% 14.71/3.26 % Equation resolutions : 0
% 14.71/3.26 % Disequality decompositions : 0
% 14.71/3.26 % Total rewrite steps : 18542
% 14.71/3.26 % ...of those cached : 15246
% 14.71/3.26 % Propositional unsat checks : 0
% 14.71/3.26 % Propositional check models : 0
% 14.71/3.26 % Propositional check unsatisfiable : 0
% 14.71/3.26 % Propositional clauses : 0
% 14.71/3.26 % Propositional clauses after purity: 0
% 14.71/3.26 % Propositional unsat core size : 0
% 14.71/3.26 % Propositional preprocessing time : 0.000
% 14.71/3.26 % Propositional encoding time : 0.000
% 14.71/3.26 % Propositional solver time : 0.000
% 14.71/3.26 % Success case prop preproc time : 0.000
% 14.71/3.26 % Success case prop encoding time : 0.000
% 14.71/3.26 % Success case prop solver time : 0.000
% 14.71/3.26 % Current number of processed clauses : 70
% 14.71/3.26 % Positive orientable unit clauses : 33
% 14.71/3.26 % Positive unorientable unit clauses: 28
% 14.71/3.26 % Negative unit clauses : 9
% 14.71/3.26 % Non-unit-clauses : 0
% 14.71/3.26 % Current number of unprocessed clauses: 40858
% 14.71/3.26 % ...number of literals in the above : 40858
% 14.71/3.26 % Current number of archived formulas : 0
% 14.71/3.26 % Current number of archived clauses : 36
% 14.71/3.26 % Clause-clause subsumption calls (NU) : 0
% 14.71/3.26 % Rec. Clause-clause subsumption calls : 0
% 14.71/3.26 % Non-unit clause-clause subsumptions : 0
% 14.71/3.26 % Unit Clause-clause subsumption calls : 739
% 14.71/3.26 % Rewrite failures with RHS unbound : 1616
% 14.71/3.26 % BW rewrite match attempts : 2005
% 14.71/3.26 % BW rewrite match successes : 337
% 14.71/3.26 % Condensation attempts : 0
% 14.71/3.26 % Condensation successes : 0
% 14.71/3.26 % Termbank termtop insertions : 3093948
% 14.71/3.26 % Search garbage collected termcells : 2
% 14.71/3.26
% 14.71/3.26 % -------------------------------------------------
% 14.71/3.26 % User time : 2.642 s
% 14.71/3.26 % System time : 0.084 s
% 14.71/3.26 % Total time : 2.726 s
% 14.71/3.26 % Maximum resident set size: 3636 pages
% 14.71/3.26
% 14.71/3.26 % -------------------------------------------------
% 14.71/3.26 % User time : 2.643 s
% 14.71/3.26 % System time : 0.089 s
% 14.71/3.26 % Total time : 2.732 s
% 14.71/3.26 % Maximum resident set size: 4864 pages
% 14.71/3.26 % E exiting
%------------------------------------------------------------------------------